B modeling
==============


Characteristics of modeling
-----------------------------------

X

Y

B0X

B1X

B0Y

B1Y

.. image:: images/100000000000045A0000024D08BDE698A920887A.png
    :width: 4.7984in
    :height: 2.5555in


.. _RefImage_100000000000045A0000024D08BDE698A920887A.png:

**Figure** 4.1-a **: B** modeling mesh**

The characteristics of B modeling are identical to those of A modeling, only the nature of the elements changes (QUAD4 instead of TRIA3).

Temporal integration:


* Diagram: NEWMARK, formulation: DEPLACEMENT,


* No time: :math:`1.{10}^{-3}s` with possible subdivision up to :math:`1.{10}^{-5}s`.


Characteristics of the mesh
----------------------------

Number of knots: 606, Number of meshes: elements QUA4: 500, elements SEG2: 210. The meshes are duplicated twice to affect the two reinforcement grids.


Tested sizes and results
------------------------------


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "Frequency (:math:`\mathrm{Hz}`) First mode", "54.67", "54.579", "0.166"
    "Frequency (:math:`\mathrm{Hz}`) Third mode", "342.64", "342.64", "338.511", "1.205"


For the transitory analysis, we test at various times (values compared to modeling B):

The average vertical movements of the points of :math:`\mathrm{B1X}`

The resultant of the nodal forces applying to :math:`\mathrm{B1X}`

The vertical nodal reaction on :math:`A`

The total kinetic energy is also tested (by comparison with the results provided by a Python loop).


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "Average vertical movements on :math:`\mathrm{B1X}` (at order number 100)", "— 7.79 10-4", "— 7.8112 10-4", "0.272"
    "Vertical resultant of the forces applied to :math:`\mathrm{B1X}` (at order number 90)", "— 9.48 10+3", "— 9.4813 10+3", "0.014"
    "Vertical nodal reaction on :math:`A` (at order number 100)", "3.72 10+3", "3.7413 10+3", "0.574"
    "Total kinetic energy (at order number 100)", "9.89588", "9.9020", "0.06"